De Morgan Application — When De Morgan s theorem is applied to a NOR function, can we obtain an equivalent expression that yields an identical truth table?

Difficulty: Easy

Correct Answer: Correct

Explanation:

Introduction: De Morgan transformations are core tools for switching between sums with inversion and products with inverted variables. Understanding how NOR relates to AND with inverted inputs lets you re-express logic while preserving functionality.Given Data / Assumptions:

  • NOR is defined as NOT (A + B + ...)
  • We assume ideal Boolean algebra over binary variables

Concept / Approach: De Morgan states: NOT (A + B) = (NOT A) (NOT B) and NOT (A B) = (NOT A) + (NOT B). Therefore, a NOR function is equivalent to an AND of complemented inputs. These two expressions generate identical truth tables because they are algebraically equivalent.Step-by-Step Solution:

Step 1: Start with X = NOT (A + B).Step 2: Apply De Morgan: X = (NOT A) (NOT B).Step 3: Conclude NOR equals AND of inverted inputs; truth tables match exactly.

Verification / Alternative check:

Construct truth tables for both forms across all 4 input pairs (00, 01, 10, 11); outputs match in every row.

Why Other Options Are Wrong:

Incorrect: Violates standard Boolean identities.Only for two inputs / Only for three or more inputs: De Morgan laws apply for any number of inputs.

Common Pitfalls:

Confusing NOR with NAND relationships.Forgetting that distribution of NOT across operators flips OR to AND and vice versa.

Final Answer:

Correct

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